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Standard XII
Physics
Dimensional Analysis
Question
The relation between force '
F
' and density '
d
' is
F
=
x
√
d
. The dimensions of
x
are:
[
L
−
1
/
2
M
3
/
2
T
−
2
]
[
L
−
1
M
1
/
2
T
−
2
]
[
L
−
1
/
2
M
1
/
2
T
−
2
]
[
L
−
1
M
3
/
2
T
−
2
]
A
[
L
−
1
M
1
/
2
T
−
2
]
B
[
L
−
1
/
2
M
3
/
2
T
−
2
]
C
[
L
−
1
M
3
/
2
T
−
2
]
D
[
L
−
1
/
2
M
1
/
2
T
−
2
]
Open in App
Solution
Verified by Toppr
The quantity is
x
=
F
√
d
Dimensions of force
F
=
[
M
1
L
1
T
−
2
]
Dimensions of density
d
=
[
M
1
L
−
3
]
Dimensions of
x
are
[
x
]
=
[
M
1
L
1
T
−
2
]
[
M
1
L
−
3
]
1
/
2
⟹
[
x
]
=
[
M
3
/
2
L
−
1
/
2
T
−
2
]
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Similar Questions
Q1
What are the dimensions of
a
and
b
in the relation
F
=
a
√
x
+
b
t
2
where
F
is force,
x
is distance and
t
is time?
View Solution
Q2
The dimension of the physical quantity
x
in the equation,
F
=
x
ρ
, where
F
is force and
ρ
is density is given by
View Solution
Q3
What is the dimensions of
A
B
in the relation
F
=
A
√
x
+
B
t
2
, where
F
is the force,
x
is the distance and
t
is the time?
View Solution
Q4
Match the following.
List I
List II
A.
Angular momentum
1.
[
M
−
1
L
2
T
−
2
]
B.
Torque
2.
[
M
1
T
−
2
]
C.
Gravitational constant
3.
[
M
1
L
2
T
−
2
]
D.
Tension
4.
M
1
L
2
T
−
1
]
View Solution
Q5
Let
F
(
x
)
=
∫
x
0
=
2
t
+
1
t
2
−
2
t
+
2
d
t
,
x
∈
[
−
1
,
1
]
then
View Solution